Describing Factorial Effects

1
Describing Factorial Effects

• Kinds of means kinds of effects
• Inspecting tables to describe factorial data
  patterns
• Inspecting line graphs to describe factorial
  data patterns
• Inspecting bar graphs to describe factorial data
  patterns
• Choosing among tables graphs

2
Interpreting Factorial Results based on
Inspection Now that we have the basic language
we will practice examining and describing main
effects and interactions based on tables, line
graphs and bar graphs portraying factorial
results. Once you know how to describe the
results based on inspection it will be a very
simple task to learn how to apply NHST to the
process. As in other designs we have looked at
an effect as a numerical difference between two
things, in factorial analyses Main effects
involve differences between marginal
means. Simple effects involve differences between
cell means. Interactions involve the differences
between simple effects.
3
Inspecting a Table to determine simple effects
interaction Task
Presentation Paper
Computer Task Difficulty Easy 90
90 Hard 50
70 Well look at
describing the interaction using each set of
simple effects in turn. Then well look at
describing each main effect (and checking if each
is descriptive or misleading)
4
Inspecting a Table to determine simple effects
interaction Simple Effects of
Task Presentation Task
Presentation Task Paper
Computer Difficulty Easy 90
90 Hard 50 70

SE of Task Pres for EasyTasks 90 vs. 90 SE
0 SE of Task Pres for HardTasks 50 vs. 70
SE 20
There is an interaction of Task Difficulty and
Task Presentation as they relate to performance.
There is no effect of presentation for easy
tasks, however for hard tasks computer
presentations led to higher scores than did paper
presentations.
5
Inspecting a Table to determine simple effects
interaction Simple
Effects of Task Difficulty Task
Presentation Task Paper
Computer Difficulty Easy 90
90 Hard 50 70

SE of Task Diff for Paper Pres. 90
vs. 50 SE 40 SE of Task Diff for Computer
Pres. 90 vs. 70 SE 20
There is an interaction of Task Difficulty and
Task Presentation as they relate to performance.
Easy tasks are consistently performed better than
hard tasks, however this effect is larger for
paper presentations than for computer
presentations.
6
Inspecting a Table to determine main effects
marginal
means for Task Difficulty Task
Presentation 90 vs. 60 Easy gt Hard Task
Paper Computer Difficulty Easy
90 90 90 Hard 50
70 60
This main effect is descriptive.. Easy gt
Hard for BOTH Paper Computer tasks
Overall, easy tasks were performed better than
hard tasks.
7
Inspecting a Table to determine main effects
marginal
means for Task Presentation
Task Presentation 70 vs. 80 Paper lt
Computer Task Paper
Computer Difficulty Easy 90
90 Hard 50
70 70 80
This main effect is potentially
misleading ... Paper lt Computer only for
hard tasks Paper Computer for
easy tasks
Overall, there was better performance on computer
than paper tasks. However, this was not
descriptive for easy tasks.
8
Inspecting a line graph Different
differences and Differential Simple Effects
both translate into NONPARALLEL LINES in a
figure. Performance Key for Task
Difficulty O Easy X Hard
90 O O 70
X 50 X 30
Paper Computer Task Presentation
P C Easy 90
90 Hard 50 70
9
Inspecting a line graph to determine simple
effects interaction Performance 90
O O Simple Effects of
Task Presentation 70
X 50 X 30 Paper Computer
Task Presentation Key for
Task Difficulty O Easy X Hard
SE of Task Pres for EasyTasks 90 vs. 90 SE
0 SE of Task Pres for HardTasks 50 vs. 70
SE 20
There is an interaction of Task Difficulty and
Task Presentation as they relate to performance.
There is no effect of presentation for easy
tasks, however for hard tasks computer
presentations led to higher scores than did paper
presentations.
10
Inspecting a line graph to determine simple
effects interaction Performance
90 O O 70
X 50 X 30 Paper
Computer Task Presentation
Key for Task Difficulty O Easy X
Hard
Simple Effects of Task Difficulty
SE Task Diff for Paper Pres. 90 vs.
50 SE 40 SE Task Diff for Computer Pres.
90 vs. 70 SE 20
There is an interaction of Task Difficulty and
Task Presentation as they relate to performance.
Easy tasks are consistently performed better than
hard tasks, however this effect is larger for
paper presentations than for computer
presentations.
11
How not to Inspect a line drawing to determine if
there is an interaction This is a cross-over
interaction -- it certainly IS an
interaction Performance but it IS
NOT the only kind !! 90 70 50 30
Paper Computer Task
Presentation Key for Task Difficulty Easy
Hard
12
Inspecting a line graph to determine if there are
main effects marginal means for Task
Difficulty Performance 90 vs. 60 Easy gt
Hard 90 O O 70
X 50 X 30
Paper Computer Task
Presentation Key for Task Difficulty O
Easy X Hard
This main effect is descriptive.. Easy gt
Hard for BOTH Paper Computer tasks
Overall, easy tasks were performed better than
hard tasks.
13
Inspecting a line graph to determine if there are
main effects Performance marginal
means for Task Pres 70 vs. 80 Paper lt
Computer 90 O O 70
X 50 X 30
Paper Computer Task
Presentation Key for Task Difficulty O
Easy X Hard
This main effect is potentially
misleading ... Paper lt Computer for hard
tasks but... Paper Computer for easy tasks
Overall, there was better performance on computer
than paper tasks. However, this was not
descriptive for easy tasks.
14
Inspecting a Bar Graph Different differences
and Differential Simple Effects both translate
into different height differences in a bar
graph. Performance 90
70 50
30 Easy Hard
Easy Hard Paper Computer
P C Task Presentation
Easy 90 90 Hard 50 70
15
Inspecting a Bar Graph to determine simple
effects interaction Different differences
and Differential Simple Effects both translate
into different height differences in a bar
graph. Performance Simple Effects of Task
Difficulty 90
70 50
30 Easy Hard Easy
Hard Paper
Computer Task Presentation

SE Task Diff for Paper Pres. 90 vs.
50 SE 40 SE Task Diff for Computer Pres.
90 vs. 70 SE 20
There is an interaction of Task Difficulty and
Task Presentation as they relate to performance.
Easy tasks are consistently performed better than
hard tasks, however this effect is larger for
paper presentations than for computer
presentations.
16
Inspecting a Bar Graph to determine simple
effects interaction Different differences
and Differential Simple Effects both translate
into different height differences in a bar
graph. Performance Simple Effects of Task
Presentation 90
70 50
30 Easy Hard Easy
Hard Paper
Computer Task Presentation
SE of Task Pres for EasyTasks 90 vs. 90 SE
0 SE of Task Pres for Hard Tasks 50 vs. 70
SE 20
There is an interaction of Task Difficulty and
Task Presentation as they relate to performance.
There is no effect of presentation for easy
tasks, however for hard tasks computer
presentations led to higher scores than did paper
presentations.
17
Inspecting a Bar graph to determine if there are
main effects Different differences and
Differential Simple Effects both translate into
different height differences in a bar
graph. Performance marginal means for
Task Presentation 70 vs. 80 Paper
lt Computer 90 70
50 30
Easy Hard Easy Hard
Paper Computer Task
Presentation
This main effect is potentially
misleading ... Paper lt Computer for only
for hard tasks Paper
Computer for easy tasks
Overall, there was better performance on computer
than paper tasks. However, this was not
descriptive for easy tasks.
18
Inspecting a Bar graph to determine if there are
main effects Different differences and
Differential Simple Effects both translate into
different height differences in a bar
graph. marginal means for Task
Difficulty Performance 90 vs. 60 Easy gt
Hard 90
70 50
30 Easy Hard Easy
Hard Paper
Computer Task Presentation
This main effect is descriptive.. Easy gt
Hard for BOTH Paper Computer tasks
Overall, easy tasks were performed better than
hard tasks.
19

• Choosing Among Tables, Line Graphs and Bar Graphs
• Tables
• Provides more detail (exact means and standard
  deviations)
• Easier to see main effects (can include marginal
  means)
• Harder to see the interaction
• Line Graphs
• Easier to see interaction pattern (than tables)
• Harder to see main effects (than tables)
• Formally limited to using when quantitative IV
  on X axis
• Bar Graphs
• Interactions -- easier than tables, not as easy
  as line graphs
• Mains -- harder to see than tables
• Note Any of these can include std, or SEM
  whiskers